What comes up, must go down.. And side to side (Newton's Second Law of Motion in 2-D); 50 minutes + 30 minute extension.
State Standards:
PS3 (9-11)–9 Students demonstrate an understanding of forces and motion by…
9b using Newton’s Laws of Motion and the Law of Conservation of Momentum to predict the effect on the motion of objects.
National Standards:
CONTENT STANDARD B: As a result of their activities in grades 9-12, all students should
develop an understanding of...
Motions and forces
Context of Lesson:
The purpose of this lesson is to further fortify the student's understanding of Newton's second law of motion. In this lesson students will begin to look at F=ma in terms of two dimensions. In doing so students will need to recall their understanding of basic trigonometry (sin, cos, etc.) and apply it to different situations to "deconstruct" their forces from polar to Cartesian coordinates. The goal is for students to achieve a significantly higher comfortableness with both Newton's second law and trigonometric identities. Some of the primary focuses of this lesson include the following:
Being able to differentiate between forces in the x-direction and y-direction
Understanding that forces in the x and y-direction cannot be combined
Continuing to develop comfortableness with polar and Cartesian conversions
Recalling what was learned from kinematics to further understand the motion of a particle due to a force
Opportunities to Learn:
Students will be able to recollect on what we learned in the previous lesson by viewing a film about the same topic from a different perspective. We will stop the video and discuss/clarify the statements in the video. Also, the students will take a formative assessment in the form of a quiz that will serve as a artifact for both the teacher and the student on their understanding and progress. Also, the class will work in large groups and vote/reason on different ideas to come up with something to present for bonus to the teacher.
Depth of Knowledge:
-As discussed in the objectives and main lesson plan, the depth of knowledge in this lesson is focused in the following categories:
Remembering
Understanding
Applying
Analyzing
Creating
Prerequisite Knowledge:
-Students will need an understanding of Newton's 2nd law provided by the previous lesson. Students will use algebra and some intuition about vectors and combining vectors.
Plans for Differentiating Instruction:
-For shy students who may not excel in the interpersonal MI, have them serve as the group leader who reports out to the teacher. For visual/spatial students, have them draw out the problems on the board for the teacher or as the group artist.
Accommodations and modifications:
Environmental factors:
Materials:
YouTube video
Books
Mini-whiteboards
Smartboard
Objectives:
Some of the key focuses of this lesson include the following:
Differentiating between forces in the x-direction and y-direction
Understanding that forces in the x and y-direction cannot be combined
Continuing to develop comfortableness with polar and Cartesian conversions
Recalling what was learned from kinematics to further understand the motion of a particle due to a force
Instruction:
Opening:
First 5 minutes of class:
Settling in and class attendance
5:00-25:00 into class:
Watch video on YouTube to recap on what we learned in the previous lesson about force (also for comic motivation).
Because the man in the video almost definitely described things in a different manner than the way i did; it would make sense to stop the video every time he deters from my previous instruction, and then clarify what he was saying briefly.
Engagement:
25:00-35:00 into class:
Introduce the students to the idea that forces can be present in both the x and y direction. Mention how F(net) is the summation of all the forces, however, you cannot combine x and y forces. This idea contains two very difficult concepts: (1) Forces can be resolved into perpendicular components, and (2) forces (and resulting changes in motion) in each direction can be analyzed independently.
This idea is usually addressed in the context of projectile motion. Have students already done this in your class? If so, are you going to go back and connect previous work to your discussion of forces? Introduce the i(hat) and j(hat) unit vectors. (If the students have never seen vectors before or are extremely weak in the field; do not stress the term unit vector. Claim that they are direction descriptors and you cannot add i's and j's together. Just i's with i's, etc.) Why introduce unit vectors? Are your students already comfortable with vectors? Does the text use unit vectors?
35:00-45:00 into class:
Work on word problems, as a class, involving forces that lay on the x and y axes (i.e. horizontal wind, gravity, etc.). Introduce a third force that lay on the x axis to explain how forces on the x axis (i-hats) can be combined, but you cannot combine them with the j-hat force (gravity). I'm glad that you see this a main point. Can students find resultant forces? Can they resolve a diagonal force into components. Students generally need a lot of practice with this.
Closure:
45:00-50:00 into the class:
Give a short quiz to the students recapping on the previous 3 lessons. With more emphasis on Newton's 1st law.
Extension:
50:00-65:00 into class:
Introduce the students to the idea of "tension" (internal force) in a problem by using example 4.3 in the book.
Make sure to specify to the students that the idea of internal force is such that the net internal force equals zero. What is an internal force? I though tension was just a force exerted by / on a rope, etc.
65:00-80:00 into class:
Using example 4.4 in the book on page 108 as a reference, explain how we as scientists sometimes describe things in the different ways.
Explain how up until this point we've used Cartesian coordinates (x and y). However, there are also situations where polar coordinates are useful.
Work on different coordinate conversion problems in the following way: As the teacher, stand next to the SmartBoard and write the problem at the top of the board. Instruct the students into two large groups (50/50); let them know they will caucus about the next step of the problem. The groups will switch off giving the next step to the teacher; if the step is correct the group gets a point. If the step is incorrect the other group has a chance to answer it. The groups will be playing for 10 extra points on quiz they took this lesson. The group who loses does not get any points but can do the step-by-step problem on the back of their next quiz for the same 10 points. Why are you introducing polar coordinates before students are comfortable with rectangular coordinates? Have they already learned these in another context. (I did not introduce polar coordinates until AP physics, i.e. in the context of rotational kinematics.)
Assessment:
The class will take a quiz on the previous 3 lessons. With more emphasis on Newton's 1st law. The quiz need be returned the next day with comments so it can be an authentic-formative assessment.
Rhode Island Department of Education Lesson Plan
Lesson Title:
What comes up, must go down.. And side to side (Newton's Second Law of Motion in 2-D); 50 minutes + 30 minute extension.State Standards:
PS3 (9-11)–9 Students demonstrate an understanding of forces and motion by…National Standards:
CONTENT STANDARD B: As a result of their activities in grades 9-12, all students shoulddevelop an understanding of...
Context of Lesson:
The purpose of this lesson is to further fortify the student's understanding of Newton's second law of motion. In this lesson students will begin to look at F=ma in terms of two dimensions. In doing so students will need to recall their understanding of basic trigonometry (sin, cos, etc.) and apply it to different situations to "deconstruct" their forces from polar to Cartesian coordinates. The goal is for students to achieve a significantly higher comfortableness with both Newton's second law and trigonometric identities. Some of the primary focuses of this lesson include the following:Opportunities to Learn:
Students will be able to recollect on what we learned in the previous lesson by viewing a film about the same topic from a different perspective. We will stop the video and discuss/clarify the statements in the video. Also, the students will take a formative assessment in the form of a quiz that will serve as a artifact for both the teacher and the student on their understanding and progress. Also, the class will work in large groups and vote/reason on different ideas to come up with something to present for bonus to the teacher.Depth of Knowledge:
-As discussed in the objectives and main lesson plan, the depth of knowledge in this lesson is focused in the following categories:Prerequisite Knowledge:
-Students will need an understanding of Newton's 2nd law provided by the previous lesson. Students will use algebra and some intuition about vectors and combining vectors.Plans for Differentiating Instruction:
-For shy students who may not excel in the interpersonal MI, have them serve as the group leader who reports out to the teacher. For visual/spatial students, have them draw out the problems on the board for the teacher or as the group artist.Accommodations and modifications:
Environmental factors:
Materials:
Objectives:
Some of the key focuses of this lesson include the following:Instruction:
Opening:
- First 5 minutes of class:
Settling in and class attendance- 5:00-25:00 into class:
Watch video on YouTube to recap on what we learned in the previous lesson about force (also for comic motivation).Because the man in the video almost definitely described things in a different manner than the way i did; it would make sense to stop the video every time he deters from my previous instruction, and then clarify what he was saying briefly.
Engagement:
- 25:00-35:00 into class:
Introduce the students to the idea that forces can be present in both the x and y direction. Mention how F(net) is the summation of all the forces, however, you cannot combine x and y forces. This idea contains two very difficult concepts: (1) Forces can be resolved into perpendicular components, and (2) forces (and resulting changes in motion) in each direction can be analyzed independently.This idea is usually addressed in the context of projectile motion. Have students already done this in your class? If so, are you going to go back and connect previous work to your discussion of forces?
Introduce the i(hat) and j(hat) unit vectors. (If the students have never seen vectors before or are extremely weak in the field; do not stress the term unit vector. Claim that they are direction descriptors and you cannot add i's and j's together. Just i's with i's, etc.) Why introduce unit vectors? Are your students already comfortable with vectors? Does the text use unit vectors?
- 35:00-45:00 into class:
Work on word problems, as a class, involving forces that lay on the x and y axes (i.e. horizontal wind, gravity, etc.). Introduce a third force that lay on the x axis to explain how forces on the x axis (i-hats) can be combined, but you cannot combine them with the j-hat force (gravity). I'm glad that you see this a main point. Can students find resultant forces? Can they resolve a diagonal force into components. Students generally need a lot of practice with this.Closure:
- 45:00-50:00 into the class:
Give a short quiz to the students recapping on the previous 3 lessons. With more emphasis on Newton's 1st law.Extension:
- 50:00-65:00 into class:
Introduce the students to the idea of "tension" (internal force) in a problem by using example 4.3 in the book.Make sure to specify to the students that the idea of internal force is such that the net internal force equals zero. What is an internal force? I though tension was just a force exerted by / on a rope, etc.
- 65:00-80:00 into class:
Using example 4.4 in the book on page 108 as a reference, explain how we as scientists sometimes describe things in the different ways.Explain how up until this point we've used Cartesian coordinates (x and y). However, there are also situations where polar coordinates are useful.
Work on different coordinate conversion problems in the following way: As the teacher, stand next to the SmartBoard and write the problem at the top of the board. Instruct the students into two large groups (50/50); let them know they will caucus about the next step of the problem. The groups will switch off giving the next step to the teacher; if the step is correct the group gets a point. If the step is incorrect the other group has a chance to answer it. The groups will be playing for 10 extra points on quiz they took this lesson. The group who loses does not get any points but can do the step-by-step problem on the back of their next quiz for the same 10 points. Why are you introducing polar coordinates before students are comfortable with rectangular coordinates? Have they already learned these in another context. (I did not introduce polar coordinates until AP physics, i.e. in the context of rotational kinematics.)
Assessment:
The class will take a quiz on the previous 3 lessons. With more emphasis on Newton's 1st law. The quiz need be returned the next day with comments so it can be an authentic-formative assessment.Reflections
(only done after lesson is enacted)Student Work Sample 1 – Approaching Proficiency:
Student Work Sample 2 – Proficient:
Student Work Sample 3 – Exceeds Proficiency: